One could say that while both schools of thought were spawned in response to the growth of western colonial power, Wahhabism is much more strongly focused on religious fundamentalism as a solution to the problems of the Muslim world. One of the questions raised by colonialism was essentially 'If God is on our side, why are we losing?' Some people said Muslims should try to emulate everything about the West, others said that Muslims should try to emulate the social structures but leave their religion as an integral part of society, and others said that god abandoned them because their faith was not pure enough. All of these ideas have their pros and cons but Wahhabism is an example of a philosophy that took the latter approach. Their political rise was on the back of the Saudis; the Saudis provided the Wahhabis with power and protection while the Wahhabis gave the Saudis a kind of moral authority. This relationship would not mean a whole lot to the rest of the world until the Saudis became extremely powerful.

Deobandism on the other hand has a more directly anti-colonialist bent. I know less about this school of thought but it's worth pointing out that it was fostered in the shadow of Great Britain's Indian empire. Obviously plenty of Wahhabis have resorted to violence to achieve their ends but in theory Deobandism is more openly endorsing of anti-colonial resistance while Wahhabists would emphasize building that perfect, pure community that lives exactly as is dictated in the Quran.

Again I am simplifying because of my own limited knowledge; inevitably there's a bit more subtlety and philosophy to these things but Wahhabism does seem to fall more along the lines of 'We must purify ourselves to be better than the West' while Deobandism is more along the lines of 'Let's inflict some violence on these guys who keep fucking with our shit.' Keep in mind that Deobandism's rise occurred during the 'Great Game' between England and Russia so the sentiment wasn't entirely unwarranted.